you'd actually have to GET a copyright on every work that you wanted to protect

Untrue. If I write something, it's already copyrighted. I don't have to get a copyright for it.

See this for more copyright myths.

Similarly (and here I'm unsure), if d33Zy's program generates something that someone else has already written, that's not in violation of copyright -- he didn't actually copy it. He'd probably have to turn up in court with all of the output of his program to prove it, though.

If, without reading a book, I somehow manage to write a word-for-word identical book, that's not violating copyright, as I understand it.